The Seagulls are unbeaten in ten Premier League games against the Hammers and are widely regarded as their bogey team.
They made the double in 2017/18 and added a 1-0 win at Amex the following season.
But after leading 0-2 in the second leg, they had to settle for a 2-2 draw.
Five more draws followed under Potter’s command before Albion’s 3-1 win at the end of last season.
Albion have taken eight points in six games against West Ham since Potter took charge.
The Seagulls boss said: “That doesn’t feel like such a great record!
“We had a lot of draws.
“I have a lot of respect and admiration for David Moyes and the work he’s done there and as a man I have a lot of time for him, I like him a lot.
“He’s a real footballer. Whenever you play his teams you can see why they achieved what they did.
“They had a difficult start. They played against Manchester City, which is never easy, and then they had the game at City Ground, but the results can look worse than they are.
“It’s an experienced squad with experienced players and an experienced coach, so we’re ready for a tough game.”
Albion last lost in the top flight to West Ham in March 1983, losing 2-1 at Upton Park despite taking the lead through Gerry Ryan after 82 minutes.
HOW ALBION DONE VS WEST HAM UNDER GRAHAM POTTER.
1:1 at home: Potter’s home debut and a first taste of VAR as Leandro Trossard ruled out a debut goal for a forensic offside against Dan Burn before later disallowing Javier Hernandez’s opener. Verdict: earned more.
3-3 away: Albion’s only glimpse of life in the relegation zone under Potter. They were 18th in the table for 18 minutes in the first half when they were 2-0 down, then were gifted an own goal, falling 3-1 behind, made two changes, through Pascal Gross and Glenn equalizing Murray’s last Prem goal – and should have won it. Verdict: Could have been worse (and better).
2:2 away: Led twice through Neal Maupay and Lewis Dunk but was penalized on set pieces. Verdict: points fallen.
1:1 at home: Percy Tau enjoyed his finest moment for Albion as his pass set up Danny Welbeck for an excellent opener before Said Benrahma equalised. Verdict: Points dropped (which might be a bit harsh).
1:1 away: Slowed down an early header from Tomas Soucek (more set piece passion) but equalized late with Maupay’s overhead kick: Verdict: point won.
3:1 at home: Another comeback from missing a rocket from Michail Antonio, thanks to goals from Joel Veltman, Gross and Welbeck to complete an all-time best result. Verdict: On cloud seven
https://www.theargus.co.uk/sport/20679889.graham-potter-says-west-ham-will-give-brighton-tough-test/?ref=rss Graham Potter says West Ham will put Brighton to the test